Evaluating the nonlinear correlation between vertical curve features and crash frequency on highways using random forests

Vertical curve features on interstate highways greatly affect traffic operations and vehicle performance and, thus, could have an impact on the occurrence of traffic crashes. Most studies to date only considered linear relationships. Though some researchers did consider nonlinearity, the preassumed data distribution may not fit the true distribution perfectly. Thus, the primary objective of this study is to develop a nonparametric algorithm to evaluate the nonlinear correlation between vertical curve features and crash frequency on interstate highways based on a random forest (RF) algorithm. Elevation data along interstate centerlines were extracted from Google Earth for two interstates in Washington State, and 5-year crash data were collected to estimate RF models for crash count prediction. A random effect negative binomial (RENB) model is employed to evaluate predictive performance. Analysis of the variables' importance shows that the proposed RF models captured the nonlinear correlation between crash count and annual average daily traffic (AADT), the elevation and grade of road segments, median lane width, left shoulder width, ratio of horizontal curve, the standard deviation of grade in 1- and 2-mi road segments, the standard deviation of elevation in 1- and 2-mi road segments, and lane width. Other variables, e.g., right shoulder width and the number of lanes on the highway were also important in the proposed RF models. By better capturing the nonlinearity, the proposed RF model outperformed the baseline model in terms of the predictive performance measurements. The findings of this research can serve to facilitate improvements in highway geometric design and recommend countermeasures to reduce the crash count on interstate highways.